The cross sections for neutrons scattering from H2 and D2 have been calculated taking into account the spin correlations, rotations, and vibrations of the molecules exactly, to the extent that the vibrations are harmonic and do not interact with the rotations. Free translations of the molecules are assumed, but this assumption is expected to be valid in the liquid, as well as the gas, for neutron energies above 0.007 eV, the Debye temperature for hydrogen. Numerical results are given for the total cross section for both orthohydrogen and parahydrogen gas at 20.4°K which agree reasonably well with the limited experimental results available. Also, curves of the double differential cross section are shown for selected incident neutron energies and scattering angles. These latter curves show very clearly the various rotational and vibrational transitions. The formulas given here are applicable at all temperatures below the thermal excitation of the first vibrational level.
The phonon spectrum of reactor grade graphite is computed by means of the essentially exact root sampling technique for a sampling 47 788 points in an irreducible segment of the Brillouin zone.
Measurements of the specific heat (over the range 100°—1000°K) are used to determine the force constants, resulting in good agreement of the calculated phonon spectrum, and neutron scattering measurements.
The lattice vibrational spectra of Be, Mg, and Zn have been obtained using the root sampling method. The force constants used in the calculations were those determined from measurements of the dispersion relations by slow neutron-scattering techniques. Calculations of the specific heat of each metal show good agreement with measured values.
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